On the computational power of sigmoid versus boolean threshold circuits
W. Maass, G. Schnitger, and E. Sontag
We examine the power of constant depth circuits with sigmoid (i.e. smooth)
threshold gates for computing boolean functions. It is shown that, for depth
2, constant size circuits of this type are strictly more powerful than
constant size boolean threshold circuits (i.e. circuits with boolean
threshold gates). On the other hand it turns out that, for any constant depth
d, polynomial size sigmoid threshold circuits with polynomially bounded
weights compute exactly the same boolean functions as the corresponding
circuits with boolean threshold gates.
Reference: W. Maass, G. Schnitger, and E. Sontag.
On the computational power of sigmoid versus boolean threshold circuits.
In Proc. of the 32nd Annual IEEE Symposium on Foundations of Computer
Science 1991, pages 767-776, 1991.